When the ISYM tag is set to 1 or 2 (by default it is set to 1), you are taking advantage of some symmetries in the charge density, and VASP will look for the symmetries of the system and apply them, so it does not matter how symmetric is your molecule. It will make the calculations faster and less resource-demanding, and will ensure that some physical properties obtained fulfill the symmetries of the system (which, if symmetrizations are switched off, may not be fulfilled due to numerical accuracy problems I guess). So, in your case, you can probably switch on the ISYM tag to 1.

However, in some cases you MUST switch off this symmetrization of the charge density. for example, calculations including Spin-Orbit coupling (SOC) must be done with ISYM=0, as the symmetry groups for systems with SOC (double groups) are not implemented in VASP, as far as I know.

For magnetic systems, the correct magnetic symmetry group is only obtained for VASP versions > 5.1, so be careful if you are running an older version of the code, specially with antiferromagnetic systems.

Also, when relaxing the ions, symmetrization may play an important role: if you start with your atoms in high-symmetric positions and ISYM is on, they will tend to stay in those symmetric positions, relaxing only in ways that do not break the initial symmetry. Thus, if you want to force the atoms into those symmetric positions, use ISYM = 1, but if you want to allow them to freely relax to any possible position, set ISYM = 0.

Additionally, I think it is sometimes not stressed out enough the importance of the SYMPREC tag. This tag sets the "tolerance" value for symmetries in your system. This means that you should use this precision when writing your atomic positions in order for VASP to correctly determine the symmetry group of the system. By default it is set to 10^-5, so even with single precision floating point numbers you should stay in the correct range, but check in the OUTCAR file if VASP has found out the correct symmetry group of your system (under the line "Analysis of symmetry for initial positions".

By the way, have you or has someone checked the difference between ISYM 1 and ISYM 2 in terms of performance and numerical accuracy? and between ISYM 0 and -1? in the VASP manual these two (-1 and 0) appear to be the same.

http://cms.mpi.univie.ac.at/vasp/vasp/ISYM_tag_SYMPREC_tag.html

Thank you Hugo for the very comprehensive reply.

Regarding the first paragraph, you said that "VASP will look for the symmetries of the system and apply them." So if VASP cannot find any symmetries and ISYM is switched on, it is will not cause problems based from my understanding. Am I correct?

Unfortunately, I am not familiar with spin orbit coupling and magnetic symmetry groups, so I can't fully comprehend your 2nd and 3rd paragraphs. But maybe someday I can use this info,

I read a book before and it said that if one is going to relax in a certain position, one should offset the position a bit to avoid very symmetric configuration. Example, if you have CO2 molecule to be relaxed on the top site, you should offset the molecule's center of gravity a bit from the center of the top site. Eventually it will return to the center of the top site, if that is really the most stable position. If I do that, I am assuming that it is not necessary to turn ISYM=0 to avoid the system from staying in very symmetric positions, since in the first place, the initial configuration has an offset from perfect symmetry. Am I right?

Thanks for the info on SYMPREC tag. The default value seems very small. Do you, in practice, vary the precision value or the default one suffices for most calculations?

I have not yet tinkered with the ISYM tag, aside from turning it on (ISYM=0) and off (ISYM=1) for a simple H2 molecule. I think my peers also do not turn this off, but then I read Computational Materials Science by June Gunn Lee and noticed that he turns it on and off depending on what he is calculating. So I wanted to learn a bit about this tag.

Thank you very much Hugo. Your answer is very helpful.

If VASP cannot find any symmetries, then your relaxation should be equivalent to one with ISYM 0. In fact, that is the idea behind moving the CO2 molecule from the top position with respect to the substrate, as in that way your system is less symmetric. A relaxation is constrained by the symmetries of the initial ionic configuration, so that if you start with a highly symmetric system, you can only end up in a configuration of the same symmetry group, as far as I know. So in short, you are right in both cases.

Regarding the SYMPREC tag, I usually take the default value, but I keep in mind that I have to write 6 or 7 decimal digits when writing a POSCAR file.

I see. Thank you very much for your answer.